# How do you find the instantaneous slope of #y=4-x^2# at x=1?

The reqd. slope

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To find the instantaneous slope of ( y = 4 - x^2 ) at ( x = 1 ), you need to find the derivative of the function with respect to ( x ) and then evaluate it at ( x = 1 ).

The derivative of ( y = 4 - x^2 ) with respect to ( x ) is ( y' = -2x ).

Evaluate ( y' ) at ( x = 1 ): ( y'(1) = -2(1) = -2 ).

Therefore, the instantaneous slope of the function ( y = 4 - x^2 ) at ( x = 1 ) is ( -2 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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